Vertex frequencies of the hierarchical dodecagonal tiling

Rubinstein, Boaz; Ben-Abraham, Shelomo I.

doi:10.1080/00150190108225115

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“…If one uses as structural models the first inflation of a square and a hexagonal lattice, the resulting compositions are BaO 46 15 and BaO 40 13 (see figure 3) respectively. Knowing the frequencies of each vertex type in the squaretriangle tiling [49], we find that a quasicrystal following the presented tiling motifs has an irrational oxygen to barium ratio, namely 3…”

Section: Geometrymentioning

confidence: 98%

Two-dimensional binary metal-oxide quasicrystal approximants

2021

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We investigate, using a systematic computational approach, the possibility of the existence of two-dimensional quasicrystalline phases of binary metal-oxides. Our approach relies on the construction of the complete two-dimensional binary phase diagram through the use of unbiased global structural prediction methods. We then identify, in the low-energy periodic phases, structural elements that can be used to generate quasicrystalline phases through an inflation process. In this way we obtain chemically consistent two-dimensional quasicrystal approximants of both barium and titanium oxides. In the proposed structures, the metallic sites occupy the vertices of the aperiodic square-triangle tiling, while the oxygen atoms decorate the interior of the polygons. We then study the properties of the approximants, both free-standing and deposited on a metallic substrate. Finally, we discuss in which circumstances the formation of these phases seems to be favored.

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Section: Geometrymentioning

confidence: 98%